Answer
Normal form of the equation of the line is:$\begin{bmatrix}{3 \\-4}\end{bmatrix} \cdot \begin{bmatrix}{x \\y}\end{bmatrix}=-5$;
General form of the equation of the line is: $3x-4y=-5$
Work Step by Step
The normal form of a line is: $n \cdot (x-p)=0$
and $n=\begin{bmatrix}{a \\b}\end{bmatrix}$
Here, $a=3, b=-4$
The normal form of the line is:$\begin{bmatrix}{3 \\-4}\end{bmatrix} \cdot \begin{bmatrix}{x \\y}\end{bmatrix}=-5$
The general form of the equation of the line is: $ax+by=c$
Thus, the general form of the equation of the line is: $3x-4y=c$
or, $3(1)-4(2)=c \implies c=-5$
Hence, the normal form of the line is:$\begin{bmatrix}{3 \\-4}\end{bmatrix} \cdot \begin{bmatrix}{x \\y}\end{bmatrix}=-5$;
The general form of the equation of the line is: $3x-4y=-5$
